Supreme Court judge Edwin Goldsbrough ruled on Friday that an absolute majority in a parliament with 51 members is 26.
If there is no appeal, or it is rejected, parliament would vote in a new prime minister.
Loughman drew Vanuatu closer to China as the previous prime minister.
He has criticised the security pact with Australia, saying it compromises Vanuatu's "neutral" status and could jeopardise development assistance from China.
The United States and its allies are seeking to dissuade Pacific Islands nations from establishing security ties with Beijing, after China signed a security pact with the Solomon Islands.
Persons:
Alatoi Ishmael Kalsakau, Eduardo Munoz, Ishmael Kalsakau, Bob Loughman, Kalsakau, Edwin Goldsbrough, Loughman, Emmanuel Macron, Macron, Kirsty Needham, Mark Heinrich Our
Organizations:
United Nations Headquarters, REUTERS, Rights, Vanuatu, Thomson
Locations:
Vanuatu, New York City, U.S, China, Australia, Western, Pacific, United States, Beijing, Solomon Islands